Physics Question from JEE Main 2025 · 4 April, Shift 1

Two slabs with square cross section of different materials $(1,2)$ with equal sides $(l)$ and thickness $\mathrm{d}_{1}$ and $\mathrm{d}_{2}$ such that $\mathrm{d}_{2}=2 \mathrm{~d}_{1}$ and $l>\mathrm{d}_{2}$. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is $\theta_{2}=2 \theta_{1}$. If the shear moduli of material $1$ is $4 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$, then shear moduli of material $2$ is $\mathrm{x} \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$, where value of x is _____ .